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    <title>orth</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>orth</b> -  orthogonal basis</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>Q=orth(A)  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>A</b>
        </tt>: real or complex matrix</li>
      <li>
        <tt>
          <b>Q</b>
        </tt>: real or complex matrix</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
      <tt>
        <b>Q=orth(A)</b>
      </tt> returns <tt>
        <b>Q</b>
      </tt>, an orthogonal
    basis for the span of <tt>
        <b>A</b>
      </tt>.  Range(<tt>
        <b>Q</b>
      </tt>) =
    Range(<tt>
        <b>A</b>
      </tt>) and <tt>
        <b>Q'*Q=eye</b>
      </tt>.</p>
    <p>
    The number of columns of <tt>
        <b>Q</b>
      </tt> is the rank of
    <tt>
        <b>A</b>
      </tt> as determined by the QR algorithm.</p>
    <h3>
      <font color="blue">Examples</font>
    </h3>
    <pre>

A=rand(5,3)*rand(3,4);
[X,dim]=rowcomp(A);X=X';
svd([orth(A),X(:,1:dim)])
 
  </pre>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="qr.htm">
        <tt>
          <b>qr</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="rowcomp.htm">
        <tt>
          <b>rowcomp</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="colcomp.htm">
        <tt>
          <b>colcomp</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="range.htm">
        <tt>
          <b>range</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
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